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针对固体火箭大气层内助推段弹道优化问题,对梯度法进行了改进。在动力学方程的线性化模型中加入控制的二阶项,从而使得在应用梯度法时不需要在目标函数中引入控制相关附加项。对上述线性时变最优控制问题进行解析求解,获得了控制曲线的最优修正。通过多次迭代修正标准控制曲线,最终获得了固体火箭大气层内助推段弹道的最优解。仿真校验表明,该方法具有计算量小、收敛速度快、对初值不敏感等优点,可运用于助推段迭代制导。
Aiming at the ballistic optimization of the boost stage in solid rocket, the gradient method is improved. The second-order term of control is added to the linearization model of the dynamic equation, so that the control-related additional term need not be introduced into the objective function when applying the gradient method. The above linear time-varying optimal control problem is solved analytically, and the optimal correction of the control curve is obtained. The standard control curve was corrected by multiple iterations, and finally the optimal solution of the projectile trajectory in the solid rocket atmosphere was obtained. The simulation results show that the proposed method has the advantages of low computational complexity, fast convergence and insensitivity to the initial value, which can be used in the iterative guidance of boost section.